Journal of Dental Materials, 2011

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Dental Materials Journal 2011; 30(6): 869880

INTRODUCTION

The restoration of endodontically treated teeth is a

challenging task that usually involves the treatment of

teeth with signicant loss of tooth structure. It has been

suggested that a post should only be used when the

remaining coronal tooth tissue can no longer provide

adequate support and retention for restoration1,2).

Nowadays, we see a variety of metallic and non-metallic

materials such as gold, titanium, stainless steel, carbon,

ceramic, zirconia and bre reinforced composites being

used for dental posts that provide retention to the core

replacing the lost coronal part of the tooth structure.

Until the mid-1980s, the indirect cast, post-core system

was considered the safest way to restore an endodontically

treated tooth3). However, the fabrication of cast posts

and cores is often a time consuming and expensive

procedure as it entails an intermediate restorative

phase. In contrast, the utilization of prefabricated posts,

combined with different types of core materials, is a

much easier process that can be performed in one visit4).

In the past, it was thought that posts reinforced

endodontically treated teeth5,6), however, other studies

have shown otherwise a post may be a predisposing

factor for root fracture7,8).

Another issue which has been widely discussed inthe literature until today is the most appropriate

material for posts9). The most highly recommended

material for reducing the risk of root fracture is exible

material that has a exible dentine-like quality with a

high Youngs modulus, such as ber-reinforced composite

posts10,11); however stress concentration may be focused

at the post-dentine interface causing debonding of the

post and movement of the core, resulting in

microleakage12). Conversely, rigid posts allow minimal

tooth preparation due to the smaller post-diameters;

however this may lead to root fracture13,14). For this

reason, clinicians (dentists) are left with two choices:

continuing to use posts with a high modulus, which could

lead to irreparable failure, or choosing low modulus posts

that can result in reparable failure9). Needless to say,

post material should be similar to dentine in modulus

elasticity exhibiting different properties at the coronal

and apical portions of the tooth for better biomechanical

performance.

The concept of functionally graded materials

(FGMs) is a new approach for the improvement of dental

post material performance compared to traditional

homogeneous and uniform materials15). This technique

allows the production of materials with very different

characteristics within the same material at various

interfaces. FGM is an innovative new technology that is

progressing rapidly in terms of the processing of

materials and the computational modeling15). It has

been found that the development of functionally graded

biomaterials for implants in medical and dental

applications allows the integration of dissimilar

materials, without severe internal stress, by combining

diverse properties into a single material16-20).

The objective of this study was to investigate thestress distribution of functionally graded dental posts

along the root canal system as compared to homogenous-

type dental posts, as well as determining the stress-

strain distribution at the post-dentine interfaces.

MATERIALS AND METHODS

Finite element modeling

Model Geometry

A three-dimensional model of a maxillary central incisor

3D-FE analysis of functionally graded structured dental posts

Noor H. ABU KASIM1, Ahmed A. MADFA1, Mohd HAMDI2and Ghahnavyeh R. RAHBARI3

1Department of Conservative Dentistry, Faculty of Dentistry, University of Malaya, Kuala Lumpur, Malaysia2Department of Engineering Design and Manufacture, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia3Department of Physics, Faculty of Sciences, University of Malaya, Kuala Lumpur, Malaysia

Corresponding author, Noor Hayaty ABU KASIM; E-mail: [email protected]

This study aimed to compare the biomechanical behaviour of functionally graded structured posts (FGSPs) and homogenous-type

posts in simulated models of a maxillary central incisor. Two models of FGSPs consisting of a multilayer xTi-yHA composite design,

where zirconia and alumina was added as the rst layer for models A and B respectively were compared to homogenous zirconia post

(model C) and a titanium post (model D). The amount of Ti and HA in the FGSP models was varied in gradations. 3D-FEA was

performed on all models and stress distributions were investigated along the dental post. In addition, interface stresses between the

posts and their surrounding structures were investigated under vertical, oblique, and horizontal loadings. Strain distribution along

the post-dentine interface was also investigated. The results showed that FGSPs models, A and B demonstrated better stress

distribution than models C and D, indicating that dental posts with multilayered structure dissipate localized and interfacial stress

and strain more efciently than homogenous-type posts.

Keywords: Heterogeneous structure, Functionally graded design, Multilayer post, Interfacial Stress, Simulated model

Color gures can be viewed in the online issue, which is avail-

able at J-STAGE.

Received Oct 4, 2010: Accepted Jul 25, 2011

doi:10.4012/dmj.2010-161 JOI JST.JSTAGE/dmj/2010-161


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was developed using Pro/Engineer software (Parametric

Technology Corporation, Kendrick St., Needham, USA),

based on the dimensions obtained from the

literature21-23). The relevant components such as the

alveolar bone, the periodontal ligament (PDL), dentine,

a post, the core, the crown and the gutta-percha were

also included in the geometric model (Fig. 1a) and their

dimensions is shown in Table 1. The geometry of the post

and core within the maxillary central incisor was

assumed to be axi-symmetrical along the vertical

centreline.

Mesh generation

Mesh generation is an important procedure that

subdivides the solid geometry of the incisor into smaller

elements. ABAQUS/CAE provides a number of different

meshing techniques. In the case of this study, a Free

meshing technique was followed that included

Table 1 Dimensions of the geometric model

Part Dimension (mm)

Crown

Height 10.5

Thickness at the top 2

Thickness at the bottom edge 1.5

Core

Height 8.5

Diameter 6

Thickness over the post 2

DentineLength 14.5

Width 8.5

Ferrule height 3

PostLength 16Diameter 1.5

Gutta-perchaLength 5Diameter 1.5

PDL Thickness 0.18

Bone Thickness 2

Fig. 1 (a) Schematic illustration of the geometric model and load directions. (b) Tetrahedral mesh structure of the geometric model.


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tetrahedral elements to separate the parts, because of

the complicated geometry of the models. This method

made it possible to achieve convergence. In addition, for

the purpose of this study, a four node, rst-order, linear

tetrahedral solid element was used (C3D4) for stress

analysis. This C3D4 incorporated a ne mesh in order to

obtain more accurate data, since constant stress on

tetrahedral elements exhibited low convergence24). After

conducting a pilot study, a tetrahedral mesh of 150465

(Fig. 1b) was used because the pilot study revealed an

error of below 0.1% for two different mesh sizes: 150465

and 239906.

Boundary condition

The boundary condition for the nodes was along the

bottom end line of the models, referred to as alveolar

bone as advocated by Yang et al.25). All components were

assumed to be perfectly bonded without any gapsbetween the components.

Three different types of loading conditions were

chosen as illustrated in Fig. 1a:

(i) A vertical load applied to the top of the crown to

simulate loading during bruxism; P1=100 N26,27).

(ii) An oblique load, angled at 45, to simulate the

masticatory force; P2=100 N26).

(iii) A horizontal load to simulate external traumatic

forces; P3=100 N26,27).

Materials and their elastic properties

A number of FGSP designs with various compositions

were investigated in a pilot study to ensure the best

combination for the FGSPs. The most signicant results

were seen in four layered FGSP, where the rst layer is

either zirconia (model A) or alumina (model B) and the

other three layers are made from xTi-yHA compositions,

as illustrated in Fig. 2. The elastic modulus of FGSPs

was estimated by applying the rule of mixture inspired

by the theory of composite materials as seen in the

following equation28):

where, (1)

1and 2are Poissons ratios for the rst and second

components in each layer.

E1 and E2 are the elastic modulus of the rst and

second components in each layer.

f1 and f2 are the volume fractions for the rst andsecond components in each layer.

The Poissons ratio for the FGSPs was also estimated

using the following formula:

(2)

The elastic properties of zirconia (in model C) and

titanium (in model D) posts and the other materials used

in the geometric models are presented in Table 2. Any

other stresses that may be introduced during the

endodontic treatment were ignored.

Ecomposite=

f1E1 +1

2

2

f2E2 2

1

=

+1 2

2

Fig. 2 Schematic illustration of the composition of the functionally graded structured posts.


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Finite element analysis

The generation of the nite element model, the

calculation of the stress distributions and the processingwere carried out using ABAQUS/CAE Professional

Version (Simulia, Valley St., Providence, USA). Stress

patterns were taken at various locations; (i) at the centre

of the posts; (ii) along the surface of the post at the

post-dentine interface and (iii) in the centre of the root

canal. The strain distribution was investigated at the

post-dentine interface and the maximum principal stress

in each component (X, Y and Z) was also studied. In

spite of this, no additional information was obtained

about the geometrical symmetry of the model along the

vertical axis (Y axis) and the direction of the exerted

loads; which are parallel, perpendicular, and oblique at

45.

RESULTS

Stress analysis under various load conditions

The maximum principle stress distributions at various

loading directions are shown in Fig. 3. The highest stress

regions are at the top of the crown and the apical part of

the root, when a vertical load was applied (Fig. 3a). On

the other hand, models C and D showed considerable

stress at the apical region of the posts (Fig. 3a).

Oblique loading caused stress to decrease

progressively from the outer to the inner part of the root

(Fig. 3b). However, it was evident that there were

differences between the stress distribution in FGSPmodels, A and B compared to models C and D, having

zirconia and titanium posts respectively. Figure 4a

shows the stress distribution in the centre of the root

canal indicating higher stress in models C and D.

Horizontal loading also showed a high level of stress

with a similar distributions pattern to oblique loading

(Fig. 3c). Moreover, stress concentration can be seen in

the centre of the root canal (Fig. 4b). When the posts

were removed, stress distribution was seen on the canal

walls, suggesting that the stress distribution was spread

over a larger area, yet the maximum principle stress was

s still within the same range (Figs. 4a and 4b).

The stress distribution along the dental posts in

models A, B, C and D when loaded vertically, obliquely

and horizontally are shown in Fig. 5. The maximumprinciple stress concentration along the post can be

observed in models C and D. In contrast, models A and

B showed a consistently lower stress distribution along

the dental posts.

Maximum principle stress and strain distributions at the

post-dentine interface

Figures 6 and 7 showed the stress and strain distributions

at the dentine-post interface. In the FGSP models, the

stress at the coronal area were negligible, while it

increased at the cervical part of the dentine ending with

gradual changes and uctuations at the apical part of

the post-dentine interface (Fig. 6). FGSP models

demonstrated less strain distribution under vertical

loading than model C and D at the apical part (Fig. 7a).

While at the junction between the middle and coronal

parts, FGSPs showed higher localized strain. For oblique

and horizontal loadings, the FGSP models demonstrated

less strain at the post-dentine interface from the cervical

part to the apical part of the dentine (Figs. 7b and c).

However, the strain distribution uctuated at the coronal

part of the FGSPs (Figs. 7b and c).

DISCUSSION

The Finite element method was used to investigate

stress in a human maxillary central incisor which hadbeen restored using various types of dental posts. A high

number of elements was used in this present study to

give a better estimation of the stress distribution.

Although Holmes et al.35), Lanza et al.36)and Zarone et

al.37)have included a cement layer in their nite element

analysis, others such as Cailleteau et al.38), Joshi et al.26)

and Toksavul et al.39) have omitted the cement layer. In

this study, the cement layer was not included as we

aimed to address the stress distribution of newly

designed dental posts. The highest value of stress

distribution was recorded at the post-dentine interface

when oblique and horizontal loadings were applied.

Table 2 Elastic properties

Materials Youngs Modulus (GPa) Poissons ratio References

Dentine 18.60 0.30 10, 29)

Titanium 116 0.33 30)

PDL 68.9103 0.40 31)

Alveolar bone 13.70 0.30 31)Gutta-percha 0.96103 0.40 10)

Zirconia 200 0.33 32)

Ceramic crown 120 0.28 33)

Composite resin core 16.60 0.24 26)

Hydroxyapatite 40 0.27 16)

Alumina 380 0.25 34)


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Fig. 3 Contour plots of the maximum principle stress distributions in models A [FGSP: zirconia/(xTi + yHA)]; B [FGSP:

alumina/(xTi + yHA)]; C [zirconia post]; D [titanium post].


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These ndings are in agreement with Zarone et al.37),

who recorded a high stress concentration at the

post-dentine interface. They also stated that when the

dental post is made from a material with a high modulus,

it will adversely alter the natural biomechanical

behaviour of the restored tooth when functioning.

Ideally, dental posts should stabilize the core and

not weaken the root40). When occlusal force is applied

coronally, the force is transferred to dentine through thecore and post system. In such situations, stress

concentrates at the cervical and apical part of the tooth.

Stress concentration at the cervical region is likely to be

due to an increase in the exure of the compromised

tooth structure, while stress concentration at the apical

region is generally due to tapering of the root canal and

the characteristics of the post41). High stress

concentrations were also observed at the apical

termination of the post42). The stiffness mismatch

between the intra-radicular post and the dental tissue

also resulted in high stress concentrations along the

post-dentine interface27). It has therefore been suggested

that an ideal dental post would have high stiffness at the

cervical region and that this stiffness should be gradually

reduced to match the dentine stiffness at the apical

end43). The compositional gradient of multilayer materials

achieved in FGMs has been identied as a possible

solution for this problem of mismatch of material

properties. Drake et al.44) used the law of power

distribution to show that signicant reduction in stress

and plastic strain can be achieved by increasing thegradient of thickness of ceramic materials and tailoring

the exponent to provide a gradual compositional change

near the parts exhibiting high modulus and little

plasticity. Matsuo et al.45) reported a reduction in the

concentration of stress at the apical area when FGM

dental posts were used.

Vertical load analysis

The highest value of maximum principle stress was

observed at the apical part of the posts in models C and

D under vertical loading. However for models A and B,

there was lower stress concentration at the apical part

Fig. 4 Contour plots of the maximum principle stresses distribution in dentine under oblique and horizontal loads for

models A [FGSP: zirconia/(xTi +yHA)]; B [FGSP: alumina/(xTi + yHA)]; C [zirconia post] and D [titanium post].


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Fig. 5 Maximum principle stress distributions along the center of the posts from coronal to

apical when loaded vertically (a), obliquely (b) and horizontally (c).


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Fig. 6 Maximum principle stress distributions at the interface between the posts and

surrounding structures from coronal to apical when loaded vertically (a), obliquely (b)

and horizontally (c).


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Fig. 7 Strain distributions at the interface between the posts and surrounding structures

from coronal to apical when loaded vertically (a), obliquely (b) and horizontally (c).


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as shown in Fig. 3a. This is due to the functionally graded

structural design of models A and B. The variation of Ti

concentration in xTi-yHA provides a smooth change in

the property of FGSPs, providing a reduction in the

stress concentration46). Thus, FGSPs were successful in

improving the stress dissipation and barring stress

propagation in the tooth structure. Figure 5a shows the

maximum principle stress concentrations along the

dental posts. FGSPs displayed better stress distribution

at the coronal and apical parts compared to homogenous

posts. Although higher stress was observed at the middle

portion of models A and B as shown in Fig. 5a, this value

can be considered as negligible compared to models C

and D. A considerably high stress concentration was

detected at the apical parts of the posts in models C and

D, which could be the reason for failure at the apical

parts and the fracture of the root in commercially

produced dental posts.

The maximum principle stress distribution in the

interface of the posts and their surrounding structure

can be seen in Fig. 6a. FGSPs dissipated interface stressexcellently from the coronal to the apical parts of the

posts. The homogenous posts, on the other hand,

transferred the stress through the whole interface, with

two points of maximum stress located at the coronal and

apical parts. The behaviour of models A and B was very

similar, while models C and D only demonstrated similar

behaviour towards the apical part of the post interface.

The strain distribution in the interface of the post

and its surrounding structure is shown in Fig. 7a.

Compared to homogenous posts, FGSPs showed less

strain values at the apical part. Localized strain values

in FGSPs showed a peak at the junction between the

coronal and the middle third, when a vertical load was

applied. The occurrence of this peak may be due to the

limitations of the FEA program where an estimate of 1

mm thickness has been used for the transition layer

between the rst and second layers (Fig. 2), assuming a

uniform composition. However, this may be inaccurate

when FGMs are fabricated. In reality, a gradual change

in the composition of the rst and second layers is

normal, resulting in what is called a transition zone.

Oblique and horizontal load analysis

The maximum principle stress was more prominent at

the outer sides of the root canal for models C and D,

compared to models A and B, as shown in Fig. 3b, c. This

is probably due to the low stiffness of the FGSPs at theapical part of the root canal. The results therefore further

substantiate the claim that FGSPs help to reduce and

dissipate stress concentration.

Stress distributions at the post-dentine interface are

illustrated in Fig. 6b, c. FGSPs dissipated or even

eliminated the interface stress from the coronal portion

to the middle part of the post. However, the interface

stress was high in the middle part of the post and

increased progressively at the apical part, uctuating in

value. In models C and D, maximum principle stress

increased dramatically throughout the interface, with a

higher intensity and uctuations in stress values at the

apical part. Similar trends were observed for oblique and

horizontal loadings for all models (Fig. 6b, c). The strain

behaviour at the middle and apical parts (Fig. 7b, c)

corresponded to the stress analyses when oblique and

horizontal loadings were applied. In the horizontal

plane, the material was distributed uniformly, i.e.there

were no changes in composition in a radial direction.

Therefore, FGSPs showed slightly more shear strain

distribution than the homogenous posts in the coronal

part.

Comparison between vertical, oblique and horizontal

loadings

Under horizontal and oblique loadings, the higher values

of maximum principle stress are distributed mainly at

the coronal and middle parts of the homogeneous posts.

Then the stress reduces dramatically in the middle part

of the posts, and becomes almost negligible at the apical

part. However under vertical loading, the concentration

of stress was low at the coronal parts but was noticeably

high at the apical parts of the model C and model Dposts. Vertical loading caused a high concentration of

stress at the apical portion of the tooth, yet under

horizontal and oblique loading, the stress became

concentrated at the outer sides of the root. Also, the

interface stress and strain increased in the middle of the

tooth and grew progressively, uctuating at the apical

part under horizontal and oblique loadings. On the

contrary, under vertical loading, the interface stress and

strain increased at the coronal part and reached its

maximum level at the apical part with little uctuation.

The concentration of stress caused by horizontal and

oblique loading was higher than that caused by vertical

loading at the apical part of the simulated posts. Thus,

horizontal loading should be avoided as much as possible.

These ndings concurred with the results reported by

Yang et al.47), who observed that greater deection and

higher stress is generated by horizontal loading. Under

horizontal and oblique loadings, post material should be

chosen carefully to ensure that the posts support the

restored tooth and prevent high stress along the inner

canal wall (Fig. 4). Ramakrishna et al.48)suggested that

dental posts should be stiff in the coronal region, i.e.the

core, so that the core is not stressed excessively when

occlusal force is applied to the crown. Hence, an ideal

dental post is one that has a high degree of stiffness at

the coronal region, and which gradually reduces to a

value similar to that of dentine at the apical end. Thishigh stiffness eradicates stress from the core, and the

gradual reduction in stiffness dissipates stress from the

post to the dentine uniformly. This gradual dissipation of

stress eliminates the concentration of stress and reduces

interfacial shear stress. For vertical loading, materials

that prevent a high concentration of stress at the apical

portion of the tooth should be chosen. In addition, the

stiffness of the entire post-core system must be able to

resist the forces of mastication, with the least possible

deformation49).


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CONCLUSION

This study shows that FGSPs exhibited several

advantages in terms of stress distribution compared to

posts fabricated from homogeneous material. The stress

and strain distribution at the post-dentine interface of

FGSPs was better than that of homogenous posts.

Functionally graded materials approach can be used to

design new dental posts that enhance the success of

endodontically treated teeth.

ACKNOWLEDGMENTS

The authors wish to sincerely thank Mr. Bernard Saw

Lip Huat, at the Department of Engineering Design and

Manufacture, Faculty of Engineering, University of

Malaya for his invaluable advice in FEA. This study was

funded by PS354/2008C, University of Malaya.

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